**Algebra
Lab - ****Comparison
of Car Fuel Economy**

by Lynn Onken

This
is a study of the fuel economy rates for two different vehicles
and the cost of fuel for each over a given time period.

Comprehension

Observations regarding the fuel economy of an automobile, designing
a model of the relationship of miles and gallons consumed

Questions

- You may
have observed the cost of fuel has been increasing over the
last few years. There are problems associated with the amount
of fuel each vehicle uses, as well as the cost to the owner.
List some of them now.
- Amount
of fuel used when driving different vehicles may be one of the
items you observed. Specifically, what do you think the relationship
between driving a four-cylinder vehicle and an eight-cylinder
vehicle is, in terms of the amount of fuel consumed
- What happens
when most of the community drives vehicles that consume a lot
of fuel?
- Who benefits
from the use of vehicles that consume a lot of fuel?
- If you
answered the previous question with “gasoline companies”, you
are right. How does a consumer drive a vehicle in the most economical
way?
- What effect
does the consumption of a great amount of fuel have on our environment?
Why?

Acquisition

Mathematical Topics

Learn or review mathematical concepts and skills needed to study
car fuel economy. See the menu at the left.

Automobiles: Part I

Information

Suppose you own a Ford Contour, four-cylinder vehicle. You are
interested in finding out the average fuel economy for your vehicle,
so you keep track of the miles you have driven, and the amount
of fuel you have used each time you get gas. The table below provides
the data you have recorded for a time period, the first column
noting the number of miles driven between fill-ups and the second
column indicating the number of gallons purchased.

Data Table

Miles
Driven |
Gallons |

262 |
10.25 |

301 |
11.80 |

347 |
11.60 |

272 |
10.50 |

368 |
12.08 |

293 |
10.08 |

Application

Apply mathematical knowledge and Tool Chest applets to analyze
the rate of fuel consumption by the Contour. Analyze the cost
of fuel for the car over a period of time.

Questions

- Make points
from the data in the table, one for each record. The first
coordinate will be the miles driven and the second coordinate
will be the number of gallons used.
- Using the
linear regression applet, plot the points for these records.
What does the data appear to do? Why do you think the graph
looks like this?
- Using the
linear regression applet, find the model of best fit. What
is the value of the coefficient of x? What does this value
represent to you, the car owner.
- If you
traveled an average of 500 miles each month for an entire year,
how many gallons of gas do you think you will use?
- If every
member of a five-person family drove an average of 500 miles
each month, assuming all drove cars with similar gas consumption
as the Contour, how much gasoline would be needed?
- Estimate
the amount of gasoline you will need for a 2000-mile trip.
- Find the
rate of change (slope) for a 1500-mile trip and the 2000-mile
trip. Compare this to the coefficient of x in your linear model.

Reflection

Examine solutions and implications.

- Do you
think the model you found accurately reflects the data?
- Will the
model always work? In what situations would the model become
invalid? For what length of time will the model remain valid?
- Why is
it important to keep records of your fuel consumed and miles
driven?
- What benefit
will this information be to you? How can you use the information
to your advantage?

Automobiles: Part II

Comprehension

Observations regarding the fuel economy of an automobile, designing
a comparison of two different vehicles, the amount of fuel used
by each.

Questions

- You may
have observed the cost of fuel has been increasing over the
last few years. There are problems associated with the amount
of fuel each vehicle uses, as well as the cost to the owner.
List some of them now.
- Amount
of fuel used when driving different vehicles may be one of the
items you observed. Specifically, what do you think the relationship
between driving a four-cylinder vehicle and an eight-cylinder
vehicle is, in terms of the amount of fuel consumed?
- What happens
when most of the community drives vehicles that consume a lot
of fuel?
- Who benefits
from the use of vehicles that consume a lot of fuel?
- If you
answered the previous question with “gasoline companies”, you
are right. How does a consumer drive a vehicle in the most economical
way?
- What effect
does the consumption of a great amount of fuel have on our environment?
Why?

Acquisition

Mathematical Topics

Learn or review mathematical concepts and skills needed to study
car fuel economy. See the menu at the left.

Information

Automobiles

Suppose you are considering owning a Chevrolet Impala, an eight-cylinder
vehicle. You currently own a Ford Contour, a four-cylinder vehicle.
You are interested in finding out the average fuel economy for
the new vehicle, A friend owns an Impala, so you obtain records
from her including the number of the miles they have driven, and
the amount of fuel they have used for these miles. The table below
provides the data you have recorded by your friend when they first
purchased the Impala.

Cumulative Data Table

Miles |
Gallons |

3072 |
208.37 |

1966 |
108.40 |

740 |
44.06 |

809 |
48.06 |

991 |
58.60 |

821 |
46.15 |

1159 |
66.48 |

Application

Apply mathematical knowledge and Tool Chest applets to analyze
the rate of fuel consumption of the Impala. Analyze the cost
of fuel for the car over a period of time.

Questions

- Make points
from the data in the table, one for each record. The first
coordinate will be the miles driven and the second coordinate
will be the number of gallons used.
- Using the
linear regression applet, plot the points for these records.
What does the data appear to do? Why do you think the graph
looks like this?
- Using the
linear regression applet, find the model of best fit. What
is the value of the coefficient of x? What does this value
represent to you, the car owner.
- If you
traveled an average of 500 miles each month for an entire year,
how many gallons of gas do you think you will use?
- If every
member of a five-person family drove an average of 500 miles
each month, assuming all drove cars with similar gas consumption
as the Contour, how much gasoline would be needed?
- Estimate
the amount of gasoline you will need for a 2000-mile trip.
- Find the
rate of change (slope) for a 1500-mile trip and the 2000-mile
trip. Compare this to the coefficient of x in your linear model.

Reflection

Examine solutions and implications.

- Do you
think the model you found accurately reflect the data on the
Impala?
- Will the
models always work? In what situations would the model become
invalid? For what length of time will the model remain valid?
- Why is
it important to keep records of your fuel consumed and miles
driven?
- What benefit
will this information be to you? How can you use the information
to your advantage? If you completed the Part I models for the
Contour as well:
- How do
the results for the Impala compare to the results for the Contour?
- If you
drove the Impala for a year, how different will your fuel consumption
be when compared to the Contour?
- What would
be the benefits to driving either vehicle? What would be the
negative aspects, particularly if you were to take a long trip?